1. Field of the Invention
The present invention relates to a method of measuring rotational and flight characteristics of a sphere and an apparatus for measuring the rotational and flight characteristics of the sphere. More particularly, the present invention relates to the method of measuring the number of rotations of the sphere such as a golf ball, the direction of the rotational axis thereof, the flight path thereof, and the flight speed thereof by specifying the three-dimensional posture and position thereof.
2. Description of the Related Art
Various methods and apparatuses for measuring the rotational amount and the like of spheres such as the golf ball are proposed.
According to a known method, light is emitted to a sphere having a reflection tape bonded to its surface or to a sphere having a non-reflecting region painted in black on its surface to thereby measure the rotational amount of the sphere, based on a change in the amount of reflection light obtained by the rotation of the sphere. However the optical amount is measured in this method, whereas the contour of the sphere and the displacement of its posture are not measured. Thus it is impossible to specify the direction of the rotational axis and the like of the sphere. Therefore normally, a sphere having a plurality of marks given to its surface is photographed at predetermined intervals while the sphere is rotating and flying to find the rotational amount of the sphere and the direction of its rotational axis, based on a displacement situation of each of a plurality of images obtained by photographing the sphere.
As apparatuses and methods of finding the rotational amount and the like of the sphere from images of the photographed mark-given sphere, the following measuring apparatuses and methods are proposed: The apparatus for measuring the rotational amount of the sphere disclosed in Registered Patent No. 2810320, the method of measuring the motion of a golf ball disclosed in Japanese Patent Application Laid-Open No. 10-186474, and the apparatus for measuring the flight characteristic of sporting goods disclosed in Registered Patent No. 2950450.
In the measuring apparatus proposed by the present applicant and disclosed in Registered Patent No. 2810320, as shown in FIGS. 12A and 12B, the sphere T, having the center C, to which the marks P and Q are given is photographed twice to obtain two two-dimensional images G1 and G2. The radius of the sphere in each of the two-dimensional images G1 and G2 is specified as the unit radius. The three-dimensional coordinates of each of the marks P and Q and the center C are computed from the two-dimensional coordinates on the two-dimensional image G1. The three-dimensional coordinates of each of the marks P′ and Q′ and the center C′ are also computed from the two-dimensional coordinates on the two-dimensional image G2. These computed three-dimensional coordinates are set as three-dimensional vectors to find the vector movement amount between the two images G1 and G2 to thereby compute the rotational amount of the sphere T and the direction of its rotational axis.
As shown in FIGS. 13A and 13B, in the measuring method disclosed in Japanese Patent Application Laid-Open No. 10-186474, the sensor 2 that detects the motion of a golf club when it hits the ball B1 is used to determine a photographing timing. The ball B1 is photographed at a predetermined interval by the first and second cameras 1A and 1B. Thereby as shown in FIG. 13B, the picture G3 in which the two balls B1 and B1′ are present is obtained. The two-dimensional ball image G3 is processed by the method similar to that of the measuring apparatus disclosed in Registered Patent No. 2810320 to compute the rotational amount of the ball and the direction of its rotational axis.
With reference to FIGS. 14A and 14B, in the measuring apparatus 4 disclosed in Registered Patent No. 2950450, the balls B2 and B2′ to which the marks Ba have been given are photographed by the synchronized cameras 5A and 5B to provide one picture in which the image of each of the balls B2 and B2′ is present. The three-dimensional coordinates of the marks Ba are obtained based on a principle similar to the triangulation by relating the principle to the relationship between the visual field of the camera 5A and that of the camera 5B. Thereby as shown in FIG. 14B, a view of the three-dimensional region of the balls B2 and B2′ is obtained to measure the characteristics of the ball. The method of obtaining the three-dimensional coordinates in this manner is known as DLT (Direct Liner Transformation).
Disclosed in Registered Patent No. 3185850 is the monitoring apparatus for measuring and displaying the flight characteristic of sporting goods. More specifically, using th shutter means, one image of a ball is obtained with at least one camera. The cameras are required to be calibrated by using more than a required number of points, having known coordinates, which are set in a space to be measured. By utilizing the relationship between known coordinates of a three-dimensional space and two-dimensional coordinates projected on the film surface of the camera, six variables (three components of coordinates of center of gravity of mass of sphere and three rotational amounts on reference coordinates) can be solved by repeatedly computing the linearity of Taylor's theorem eight times. It is possible to obtain three-dimensional coordinates of marks fixed to the ball by setting the length of an actual space as the reference not the radius of the ball image. Therefore it is unnecessary to correctly photograph the contour of the ball. Further it is possible to alleviate the problem of shortage of brightness that is caused by a high-speed shutter means for obtaining a still image of the ball flying at a high speed. The monitoring apparatus improves the degree of freedom of photographing equipment.
As disclosed in Registered Patent No. 2626964, the present applicant proposed a method of measuring the position and the driving angle of a spherical object. The method is carried out by a projection apparatus that projects a plurality of parallel beams of light and by a plurality of light-receiving apparatuses that detect incidence and shielding of light projected by the projection apparatus. The period of time in which the light beams are shielded is measured by using the distance between a ball and a plane where the projection apparatus and the light-receiving apparatuses are disposed, the position of light beams shielded after the ball was impacted, dimensions between light beams, and the diameter of the ball. Thereby it is possible to determine the height position of the center of the ball and the deviation position thereof. Thereby the driving angle and deviation angle of the ball can be measured.
In the measuring apparatus shown in FIGS. 12A and 12B and the measuring method shown in FIGS. 13A and 13B, because the radius of the sphere image is used in computations for measurement, the accuracy of the three-dimensional vector to be computed depends on the accuracy of the radius of the sphere image. Thus it is necessary to highly accurately photograph the sphere to obtain its image on the basis of which the measurement is made. It is also necessary to find the radius of the sphere with high accuracy from the photographed images. To obtain a still image of the sphere flying at a high speed, it is necessary to use a high-speed camera having a high-speed shutter. However because the high-speed shutter opens in a very short period of time, it is difficult to obtain a sufficient amount of light.
The sphere image is comparatively clear in the vicinity of the center thereof because the center of the ball confronts the camera. On the other hand, it is difficult to clearly capture the contour of the sphere. Even though the manner of emitting light to the sphere is adjusted, it is difficult to solve this problem. Consequently the contour of the image of the sphere is unclear. Thus the radius of the image is read with low accuracy, which causes the rotational amount of the sphere and the like to be measured with low accuracy.
In the measuring apparatus shown in FIGS. 14A and 14B, the three-dimensional coordinates of the marks given to the surface of the ball are obtained not by using the radius of the ball image but on the basis of the length of an actual space. Thus it is unnecessary to photograph the contour of the ball clearly, and the problem of shortage of luminous intensity rarely occurs. Further the measuring apparatus shown in FIGS. 14A and 14B has an advantage of reducing a burden on the measuring equipment. However, to find the three-dimensional coordinates of the marks given to the surface of the ball with high accuracy, it is necessary to obtain images of the ball in a comparatively large size to allow the marks to be read accurately. To photograph the ball in a large size, it is necessary to obtain the two images of the ball by photographing it at a short interval, which reduces the rotational amount of one ball image with respect to that of the other ball image.
To measure the rotational amount of the ball with high accuracy, it is necessary to increase the moving distance of each mark to thereby increase the displacement of the position of the mark, i.e., increase the rotational amount of one ball image with respect to that of the other ball image, which necessitates a condition reciprocal to the increasing of the ball image.
Thus it is possible to measure the three-dimensional coordinates of the marks with high accuracy by increasing the ball image. However, because the change of the positions between both images is small, the rotational amount of the ball cannot be measured with high accuracy. In the case where the ball is photographed in such a way as to increase the rotational amount of the other ball image with respect to that of the one ball image, it is necessary to photograph the ball at a long interval. In this case, although the rotational amount of the ball can be measured with high accuracy, the ball images are small. Therefore the three-dimensional coordinates of the marks are measured with low accuracy. Thus the measuring apparatus is incapable of measuring both the three-dimensional coordinates of the marks and the rotational amount of the ball with high accuracy.
To solve the above-described problem, it is conceivable to prepare two sets of measuring apparatuses to obtain one image of the ball with a first measuring apparatus and the other image thereof with a second measuring apparatus to measure both the three-dimensional coordinates of each mark and the rotational amount of the ball with high accuracy. However in carrying out measurement, it is necessary to make a calibration by associating the operation of four cameras of both sets of the measuring apparatuses with each other. Furthermore the measuring apparatus is required to have a very complicated construction and is hence very expensive. As such, it is difficult to use two sets of the measuring apparatuses.
Further in computing the rotational amount of the ball from the movement amount of the mark given to the surface of the photographed ball, it is necessary to recognize which of marks present on another image of the ball is coincident with a particular mark present on one image thereof. In the case where the direction of the rotational axis of the ball can be estimated, and the change of the rotational amount of another ball image with respect to that of the one ball image is small, it is comparatively easy to recognition of the particular mark. However in the case where the direction of the rotational axis of the ball cannot be estimated because the direction of the rotational axis of the ball changes greatly in each measurement or in the case where the change of the rotational amount of another ball image with respect to that of the one ball image is large, it is very difficult to accomplish the recognition of the particular mark. In this case, there is a possibility that the rotational amount of the ball and the like cannot be measured by means of an automatic recognition program of a computer. In the case where a man recognizes the particular mark, it takes much time and may make an erroneous recognition of the particular mark.
In addition, it is impossible to make measurement in the case where the mark which has appeared on the one ball image rotates to the reverse side of another ball image and does not appear on the surface thereof. In this case, there is a limitation in the measuring direction of the camera and the rotational direction of the ball. Thus the measuring apparatus has a problem of having difficulty in making measurement in an optimum situation.
In the monitoring apparatus disclosed in Registered Patent No. 3185850, the mark that is seen on one ball image is not present on another ball image in dependence on a rotation angle of the ball. That is, in the case where the mark which is present on the one ball image rotates to the reverse side of another ball image, it is impossible to measure the flight characteristic of the ball. Thus there is a limitation in the photographing direction of the camera and the rotational direction of the ball. Further the monitoring apparatus is inferior in portability.
In Registered Patent No. 2626964, it is possible to measure a passage position of the spherical object widely and accurately without contact when it is flying. However, there is a room for improvement in the method of computing the spin amount of the spherical object.